This invention relates to a method of flaw characterization by multiple angle inspection using ultrasound and a limited-angle reconstruction procedure.
Ultrasound is frequently used to locate and characterize flaws in nondestructive testing. However, present state-of-the-art techniques generally do not allow one to determine the identity, shape, and orientation of a flaw if its size is smaller than the ultrasound beam diameter. The current accuracy of the size and composition estimates of a flaw depends on the ratio of the characteristic size of the flaw to the beam diameter. For a flaw having a size larger than the beam diameter, its dimension can be estimated by laterally scanning an acoustic microscope around the flaw location in what is usually referred to as a c-scan. However, this c-scan estimation is not practical for a flaw having a size smaller than the beam diameter. Instead, composition and geometrical parameters of these flaws are often estimated from the acoustic scattering pattern.
Flaw characterization is an inversion problem in which the parameters of the flaw such as its type, elastic constants, shape, size, orientation, etc., are deduced from the scattering amplitude measurements. In general, no explicit expression of flaw parameters in terms of scattering amplitudes is available. The relation between the scattering amplitude of the acoustic waves and the flaw parameters can be expressed by the integral equation in tensor notation as developed in Gubernatis, J.E., Domany, E and Krumhansl, J.A., "Formal Aspects of the Theory of the Scattering of Ultrasound by Flaws in Elastic Materials", J. Appl. Phys., 48 (1977) 2804. The exact solution for the integral equation for general cases does not yet exist. As a result, one has to resort to particular cases and approximation methods. In the three-dimensional inverse Born approximation, it can be shown that for incident plane wave and for isotropic homogeneous medium and flaw, the back-scattered amplitude A (.omega., .OMEGA.) can be written in the form: EQU A(.omega.,.OMEGA.)=.omega..sup.2 F({.mu.})S(2.omega./v,.OMEGA.)(1)
Where F is a function of {.mu.} which denotes collectively the material parameters of the medium and the flaw, and S is equal to the Fourier transform of the characteristic function of the flaw in the direction .OMEGA. of the incident plane wave, Rose, J.H. and Krumhansl, J.A., "Determination of Flaw Characteristics from Ultrasonic Scattering Data", J. Appl. Phys., 50 (1979) 2951. The characteristic function as defined is equal to 1 inside the flaw and equal to 0 outside the flaw. From equation (1) one obtains S as follows: EQU S(.omega./v,.OMEGA.)=4A(.omega./2,.OMEGA.)/[.omega..sup.2 F({.mu.})](2)
The Fourier transform of the flaw characteristic function therefore can be obtained by superimposing the quantity S in all incident directions and from which the characteristic function itself can be reconstructed by inverse Fourier transformation. The Lame material constants of the flaw can also be obtained in the process.
In general, it is not feasible to inspect a flaw from all incident angles. As a result, the Fourier transform of the characteristic function would have missing components in some angular range. These missing components give rise to artifacts in the reconstructed characteristic function. Partly because of the impracticality of viewing from all incident directions and partly because of the complexity of the three-dimensional reconstruction procedure, the method is usually simplified and restricted to characterize the class of ellipsoidally shaped flaws. For this class of flaws, one can obtain all relevant information about the flaw from a small number of back-scattered waveforms. This significantly simplifies the application of the procedure. This simplified procedure is known as the one-dimensional inverse Born approximation, see Rose, J.H., Eisley, R.K., Tittman, B., Varadan, V.V., and Varadan, V.K., "Inversion of Ultrasonic Scattering Data", in Acoustic, Electromagnetic and Elastic Wave Scattering, V.V. Varadan and V.K. Varadan (Eds.), Pergamon, N.Y., 1980. Though the procedure is simple, it cannot be applied to characterize flaws of general shape.
Limited-angle reconstruction techniques have been developed to remove artifacts due to missing information. Such techniques are discussed, for example, in Tam, K.C., and Perez-Mendez, V., "Tomographical Imaging with Limited-Angle Input", J. Opt. Soc. Am., 71 (1981) 582, coauthored by the present inventor. Typically, the limited-angle image reconstruction techniques make use of available a priori information of the object to compensate for the missing information that is due to restrictions on the scan. The most readily available a priori information include the external boundary of the object, and the known upper and lower bounds of the density values. Greater precision in knowledge of the a priori information provides better quality in the reconstructed images of the object which is being inspected. However, the images reconstructed in this way are usually not as good as images reconstructed from complete angular scanning information.
A method for improvement of images reconstructed from limited-angle information makes use of multiple energy x-ray scanning as taught in the inventor's Patent 4,506,327 entitled "Limited-Angle Imaging Using Multiple Energy Scanning". The method is for composite objects, such as industrial products and equipment, which are made of a small number of substances. The object is scanned several times by x-rays at different energies. By suitably combining the scanning data, the different components within the object can be constructed individually to result in much better image quality. However, the method cannot be used if it is impractical to perform multiple energy x-ray scannings.